Primitive cubic crystal

Primitive cubic crystal lattice. One unit cell is marked... 

What is the sequence of the following reflections in a primitive cubic crystal 220, 300, and 2117... 

Figure 11.1 Glide and climb of edge dislocation in primitive cubic crystal (b = [600],...

Next consider NisAl designated as LI2 or cP4. The L designates an alloy, but unless one were familiar with Strukturbericht notation, it would be necessary to look up the stiucture in a catalog of Strukturbericht crystal structures such as the Naval Research Laboratory online catalog of crystal structures (www.nrl.navy.mil/lattice/). The Pearson symbol is perhaps more informative, telling us we have a primitive cubic crystal with four atoms per unit cell, and with a little imagination, one could guess that A1 atoms must occupy the comers while Ni atoms sit on the six faces. 

The metal polonium (which was named by Marie Curie after her homeland, Poland) crystallizes in a primitive cubic structure, with an atom at each corner of a cubic unit cell. The atomic radius of polonium is 167 pm. Sketch the unit cell and determine (a) the number of atoms per unit cell (b) the coordination number of an atom of polonium (c) the length of the side of the unit cell. 

The pattern of observed lines for the two other cubic crystal systems, body-centred and face-centred is rather different from that of the primitive system. The differences arise because the centring leads to destructive interference for some reflections and these extra missing reflections are known as systematic absences. 

Definitive x-ray diffraction data on structure I was obtained by McMullan and Jeffrey (1965) for ethylene oxide (EO) hydrate, as presented in Table 2.2a. The crystal consists of a primitive cubic lattice, with parameters as given in Table 2.2a. The common pictorial view of structure I is presented in Figure 1.5a. In that figure, the front face of a 12 A cube is shown, with two complete 51262 (emphasizing hydrogen bonds) connecting four 512. 

Cl-. The lattice type is reduced from face-centered cubic to primitive cubic, and the space group of CsCl is 0 - Pm3m. Figure 10.3.3(a) shows a unit cell in the crystal structure of CsCl. 

Below 249 K, the molecules are orientated in an ordered fashion, and the symmetry of the crystal is reduced from a face-centered cubic lattice to a primitive cubic lattice. At 5 K, the crystal structure determined by neutron diffraction yielded the following data space group Pa3 (no. 205), a = 1404.08 (1) pm C-C bond lengths (6/6) 139.1 pm, (6/5) 144.4 pm, and 146.6 pm (mean 145.5 pm). 

Crystal structure of MOF-5. (a) Z114O tetrahedra joined by benzenedicarboxylate linkers. H atoms are omitted for clarity, (b) The topology of the framework (primitive cubic net) shown as an assembly of i/iu (>)()— clusters (represented as truncated tetrahedra) andp-phenylene (-CgFLj-) links (represented by rods). From O. M. Yaghi, M. O Keeffe, N. W. Ockwig, H. K. Chae, M. Eddaoudi, and J. Kim, Nature 423, 705-14 (2003). 

L. Pauling, Icosahedral quasicrystals are twins of cubic crystals containing large icosa-hedral clusters of atoms The 1012-atom primitive cubic structure of Al6CuLi3, the C-phase of Al37Cu3Li2iMg3, and GaMg2Zn3. Proc. Natl. Acad. Sd. (USA) 85, 3666-3669 (1988). 

Figure 2.t. The crystal structure of CeO> (a) unii celt as cep array of cerium atoms The cep layers are parallel to the [Ml] planes of the fe e. unit cell, (b) and (c) the same stniclure redrawn as a primitive cubic array of oxygens. 

The regular orbit displayed in Figure 2.7, is the geometry on the unit sphere such that the bond length , the Euclidean distance between adjacent vertices, is constant. This restriction is not necessary from a symmetry viewpoint it may be relaxed subject only to the requirement that the local four, three and two-fold symmetries are maintained. One important example of such a relaxation occurs for the regular orbit of the Oh Crystallographic point group. In the simplest model crystal of Oh point symmetry, the primitive cubic array, for example, as in cubium, lattice points are distributed as dictated by the lattice vector Rmnp such that... 

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